Heat flows for a nonconvex Signorini type problem in $$ {mathbb{R}^{N}} $$

We prove the existence of a global heat flow u : Ω ×  mathbbR⁺ ? mathbbR^N {mathbb{R}^{+}} to {mathbb{R}^{N}}, N > 1, satisfying a Signorini type boundary condition u(∂Ω ×  mathbbR⁺ {mathbb{R}^{+}}) ⊂  mathbbRⁿ {mathbb{R}^{n}}), n geqslant 2 n geqslant 2 , and mathbbR^N {mathbb{R}^{N}}) with boundary ∂ [`(W)] bar{Omega } such that φ(∂Ω) ⊂ mathbbR^N {mathbb{R}^{N}} is given by a smooth noncompact hypersurface S. Bibliography: 30 titles.